## Question 3:

**Either:**
$|2x-1| \geq 4$
$\Rightarrow 2x - 1 \geq 4$ | M1 (1.1) |
or $\quad 2x - 1 \leq -4$ | M1 (1.1) |

**Or:**
$(2x-1)^2 \geq 16$ | M1 (1.1) | M1 for sketch of $y=(2x-1)^2$ and $y=16$
$4x^2 - 4x - 15 \geq 0$
$(2x-5)(2x+3) \geq 0$ | M1 (1.1) | M1 for $x = 2\frac{1}{2},\ -1\frac{1}{2}$
$\Rightarrow x \geq 2\frac{1}{2}$ | A1 (1.1) |
$\Rightarrow x \leq -1\frac{1}{2}$
$\{x: x \leq -1\frac{1}{2}\} \cup \{x: x \geq 2\frac{1}{2}\}$ | A1 (2.5) | OR $x \geq 2\frac{1}{2}$ or $x \leq -1\frac{1}{2}$; if final answer not in one of these forms then withhold final A1
**Total: [4]**

---